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Physical Review A

Role of degenerate Zeeman states in the storage and retrieval of light pulses

Pei-Chen Guan, Yong‐Fan Chen, Ite A. Yu

Published Jan 22, 2007• 17 citations
Publisher

Abstract

We have studied the role of degenerate Zeeman states in the storage and retrieval of light pulses in the three-level $\ensuremath{\Lambda}$-type system of electromagnetically induced transparency. A probe pulse with the ${\ensuremath{\sigma}}_{+}$ polarization is stored in the medium and subsequently released with the ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarization. However, the manipulation of the retrieved polarization causes an energy loss. Our study shows that the incompatibility between the stored ground-state coherence and the ratio of the probe and coupling Clebsch-Gordan coefficients is responsible for the energy loss. Such energy loss can be avoided as long as all population accumulates in a single Zeeman state. We provide the useful knowledge for the light-storage technique and demonstrate that the degenerate Zeeman states should be considered in the relevant applications.

DOI
10.1103/physreva.75.013812

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We have studied the role of degenerate Zeeman states in the storage and retrieval of light pulses in the three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type system of electromagnetically induced transparency. A probe pulse with the \ensuremathσ+{\ensuremath{\sigma}}_{+}\ensuremathσ+​ polarization is stored in the medium and subsequently released with the \ensuremathσ\ensuremath−{\ensuremath{\sigma}}_{\ensuremath{-}}\ensuremathσ\ensuremath−​ polarization. However, the manipulation of the retrieved polarization causes an energy loss. Our study shows that the incompatibility between the stored ground-state coherence and the ratio of the probe and coupling Clebsch-Gordan coefficients is responsible for the energy loss. Such energy loss can be avoided as long as all population accumulates in a single Zeeman state. We provide the useful knowledge for the light-storage technique and demonstrate that the degenerate Zeeman states should be considered in the relevant applications.
Coherent optical memory based on electromagnetically induced transparency (EIT) offers a convenient way to convert the frequency or polarization of an optical probe pulse by storing in one $\mathrm{\ensuremath{\Lambda}}$ system and retrieving in another $\mathrm{\ensuremath{\Lambda}}$ system. We present a theoretical study on the efficiency variation of such an EIT-memory-based optical converter in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affect the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficients for the probe and control transition in the reading channel, which results in a nonadiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a ${\ensuremath{\sigma}}^{+}$-polarized pulse and retrieving with ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.
Memory-based optical polarization conversion in a double-Λ\LambdaΛ atomic system with degenerate Zeeman states
Abstract Optical memory based on the electromagnetically induced transparency (EIT) in a double- Λ\LambdaΛ Λ atomic system provides a convenient way to convert the frequency, bandwidth or polarization of an optical pulse by storing it in one Λ\LambdaΛ Λ channel and retrieving it from another. This memory-based optical converter can be used to bridge the quantum nodes which have different physical properties in a quantum network. However, in real atoms, each energy level usually contains degenerate Zeeman states, which may lead to additional energy loss, as has been discussed in our recent theoretical paper (Tsai et al. in Phys. Rev. A 100, 063843). Here, we present an experimental study on the efficiency variation in the EIT-memory-based optical polarization conversion in cold cesium atoms under Zeeman-state optical pumping. The experimental results support the theoretical predictions. Our study provides quantitative knowledge and physical insight useful for practical implementation of an EIT-memory-based optical converter.
We study the propagation of coherent light pulses in a medium of three-level atoms with degenerate ground- and excited-state sublevels in an electromagnetically induced transparency (EIT)-type configuration. Both the strong control field and the weak probe pulse have elliptical polarization, which gives rise to concurrent multipath couplings between the ground-state sublevels and the auxiliary stable state. We derive the probe field susceptibility and show that in general, the probe field propagates in two separate polarization modes, one of which is attenuated, the other of which displays EIT. This generic result is valid provided the atomic medium is prepared to be in a pure quantum state over the ground-state sublevels initially. We also investigate the case when the initial state of the medium is described by an incoherent mixture of ground-state sublevels and show how EIT-like pulse propagation degrades. The possibility of controlling the probe susceptibility matrix with control field polarization provides a convenient tool for probing the quantum state of the medium on the degenerate ground-state sublevels.
We propose a transformation method that simplifies quantitative analysis in the $\ensuremath{\Lambda}$-type electromagnetically induced transparency (EIT) system containing degenerate Zeeman states. This transformation maps several coupled three-state systems into a simple three-state system. Moreover, we demonstrate that the transformation is an excellent approximation under adiabatic conditions and the calculation results from several coupled systems are in good agreement with those from the simple system. The transformation method is a powerful tool for relevant studies of EIT, slow light, and storage of light.